Linear Codes over $\mathbb{F}_{q}[x]/(x^2)$ and $GR(p^2,m)$ Reaching the Griesmer Bound
Information Theory
2016-12-06 v1 math.IT
Abstract
We construct two series of linear codes over finite ring and Galois ring respectively reaching the Griesmer bound. They derive two series of codes over finite field by Gray map. The first series of codes over derived from are linear and also reach the Griesmer bound in some cases. Many of linear codes over finite field we constructed have two Hamming (non-zero) weights.
Cite
@article{arxiv.1612.01096,
title = {Linear Codes over $\mathbb{F}_{q}[x]/(x^2)$ and $GR(p^2,m)$ Reaching the Griesmer Bound},
author = {Jin Li and Aixian Zhang and Keqin Feng},
journal= {arXiv preprint arXiv:1612.01096},
year = {2016}
}